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Accurate state estimation is crucial for legged robot locomotion, as it provides the necessary information to allow control and navigation. However, it is also challenging, especially in scenarios with uneven and slippery terrain. This…

Multi-modal sensor integration has become a crucial prerequisite for the real-world navigation systems. Recent studies have reported successful deployment of such system in many fields. However, it is still challenging for navigation tasks…

Existing LiDAR-Inertial Odometry (LIO) systems typically use sensor-specific or environment-dependent measurement covariances during state estimation, leading to laborious parameter tuning and suboptimal performance in challenging…

This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a…

Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…

We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…

This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight…

Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…

In this article, we propose a new filtering algorithm based in the Koopman operator, showing that a nonlinear filtering problem can be seen as an equivalent problem where the dynamics is infinite dimensional, but linear. Using Extended…

Localization and tracking are critical components of integrated sensing and communication (ISAC) systems, enhancing resource management, beamforming accuracy, and overall system reliability through precise sensing. Due to the high path loss…

The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is designed to estimate an arbitrary continuous-time Markov diffusion process X subject to nonlinear discrete-time observations. The GI Filter is fundamentally different…

We present a cost-efficient and versatile method to map an unknown 3D freeform surface using only sparse measurements while the end-effector of a robotic manipulator moves along the surface. The geometry is locally approximated by a plane,…

A Kalman filter can be used to determine material parameters using uncertain experimental data. However, starting with inappropriate initial values for material parameters might include false local attractors or even divergence. Also,…

The main contribution of this paper is an invariant extended Kalman filter (EKF) for visual inertial navigation systems (VINS). It is demonstrated that the conventional EKF based VINS is not invariant under the stochastic unobservable…

The estimation of spatiotemporal data from limited sensor measurements is a required task across many scientific disciplines. The sensor selection problem, which aims to optimize the placement of sensors, leverages innovations in greedy…

We investigate the combined use of a Kinect depth sensor and of a stochastic data assimilation method to recover free-surface flows. More specifically, we use a Weighted ensemble Kalman filter method to reconstruct the complete state of…

Objective Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to EEG. However, this approach lacks a reliable method to determine the initial filter conditions and…

A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic…

This work introduces LIMOncello, a tightly coupled LiDAR-Inertial Odometry system that models 6-DoF motion on the $\mathrm{SGal}(3)$ manifold within an iterated error-state Kalman filter backend. Compared to state representations defined on…

In this paper we describe improvements to the particle swarm optimizer (PSO) made by inclusion of an unscented Kalman filter to guide particle motion. We demonstrate the effectiveness of the unscented Kalman filter PSO by comparing it with…